6TA.21.3.2022_Practice

6TA Practice 21.3.2022

By Ngo Van Minh

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Find a three-digit number, such that this number is equal to 5 times the product of its digits.

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What is the smallest positive integer that has 12 different positive divisors, including 1 and itself?

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Among all four-digits numbers with 3 as their thousands-digits, how many have exactly two identical digits? 

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In the box there are balls that are identical in shape, there are 5 non-Green balls, 6 non-red balls and 7 non-yellow balls. How many ways are there to draw at least 1 ball out of the box?

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Given a square ABCD with center O and AB=10. Angle EOF=90 degrees. Find the shaded area?

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What is the perimeter of the outer rectangle? All angles shown are right angles.

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Try to place 5 points in (or on the perimeter of) an equilateral triangle with side length 20, as to maximize the distance between the points. What is the greatest possible distance between the two closest points?

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Each side of a square ABCD is coloured by one of four colours: red, blue, green or yellow. In how many different ways can we colour the 4 sides of the square such that any two adjacent sides have different colors?

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How many positive integers less than or equal to 2016 are multiples of 3 or 4 but not 5?